Subject: General Aptitude · Chapter: Number System · Exam: · Marks: · Difficulty:
What is the remainder when $17{ }^{36}$ is divided by 36?
(a)1
(b)7
(c)19
(d)29
Answer
Answer (as printed): A
Explanation
$17^{36}=\left(17^{2}\right)^{18}=(289)^{18}$. Now, [(289) ${ }^{18}$ - 1] is divisible by (289 - 1), i.e. 288 $\Rightarrow\left(17^{36}-1\right)$ is divisible by 288 and hence by 36 ⇒ On dividing $17^{36}$ by 36, we get 1 as remainder.
Explanation as extracted from the printed page; notation may be imperfect.